Question: A cup of hot coffee has been left to cool in a room with an ambient temperature of $21^\circ{\text{C}}$. The relationship between the elapsed time, $m$, in minutes, since the coffee was left to cool, and the temperature of the coffee, $T$, measured in $^\circ C$, is modeled by the following function. $T(m)=21+74 \cdot 10^{-0.03m}$ What will the temperature of the coffee be after $10$ minutes? Round your answer, if necessary, to the nearest hundredth.
Thinking about the problem We want to find the temperature of the coffee after $10$ minutes. In other words, we are given an $m$ value of $10$ minutes and want to find the temperature associated with that input, or $T(10)$. To do this, we can substitute ${10}$ in for $ m$ and evaluate. $T({10})=21+74 \cdot 10^{-0.03({10})}$ Evaluating the expression We can use a calculator to evaluate the expression. The answer is shown below. $\begin{aligned}T(10)&=21+74\cdot 10^{{-0.03(10)}}\\\\ &=21+74\cdot 10^{{-0.3}}\\\\ &\approx58.09\\\\ \end{aligned}$ After $10$ minutes, the temperature of the coffee will be $58.09$ $^\circ C$.